My computer NEVER boots up first time. When I press the On button, it will stall and the monitor light will just continue flashing. I then have to keep retrying the On/Off Button until I hear 2 "blips" from inside my tower, then I know it will boot up fine. If it just does 1 "blip", 99% of the time it won't boot up.

Second:

This has only happened since I have re-formatted my computer. When I play a STEAM game, occasionally it will feel like my mouse has frozen. The graphics are still in motion and the sound is fine, but I can't control anything or press anything. This will last for a second or two. I've come to notice that this mostly happens the FPS is dropping or there's a lot going on at once.

I've tried uninstalling and reinstalling my graphics drivers multiple times (same thing happening no matter which I use), and reinstalling STEAM. All my other drivers are fully up to date and working so I put this down to a hardware fault.

One
Thats Strange, On Award and AMI BIOS'es (And others) 1 Beep should indicate a successful POST while 2 beeps should indicate A Parity circuit failure...
I would try a BIOS Flash. Which would require YOU to goto the manufactures site of that motherboard locate the specific model, download BIOS Flash File and follow instructions on website.

two
Update Game patch, try Lowering or changing combinations of video settings, reinstall/update mouse software or driver. Update USB Driver if mouse is attached by USB.